Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes
文献类型：期刊论文
| 作者 | Qiu, Yanqi1,2; Wang, Zipeng3 |
| 刊名 | JOURNAL OF FUNCTIONAL ANALYSIS
 |
| 出版日期 | 2022 |
| 卷号 | 282期号:1页码:45 |
| 关键词 | Hyper-positivity Positive definite kernel Herglotz-Bochner theorem Hypercontractivity |
| ISSN号 | 0022-1236 |
| DOI | 10.1016/j.jfa.2021.109266 |
| 英文摘要 | We propose a definition of branching-type stationary stochastic processes on rooted trees and related definitions of hyper-positivity for functions on the unit circle and functions on the set of non-negative integers. We then obtain (1) a necessary and sufficient condition on a rooted tree for the existence of non-trivial branching-type stationary stochastic processes on it, (2) a complete criterion of the hyper-positive functions in the setting of rooted homogeneous trees in terms of a variant of the classical Herglotz-Bochner Theorem, (3) a prediction theory result for branching-type stationary stochastic processes. As an unexpected application, we obtain natural hypercontractive inequalities for Hankel operators with hyper-positive symbols. (C) 2021 Elsevier Inc. All rights reserved. |
| 资助项目 | National Natural Science Foundation of China[NSFC Y7116335K1] ; National Natural Science Foundation of China[NSFC 11801547] ; National Natural Science Foundation of China[NSFC 11688101] ; NSFC[11601296] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000709435800010 |
| 出版者 | ACADEMIC PRESS INC ELSEVIER SCIENCE |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/59447]  |
| 专题 | 中国科学院数学与系统科学研究院 |
| 通讯作者 | Qiu, Yanqi |
| 作者单位 | 1.Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China 2.Chinese Acad Sci, AMSS, Inst Math, Beijing 100190, Peoples R China 3.Chongqing Univ, Coll Math & Stat, Chongqing 400044, Peoples R China |
| 推荐引用方式 GB/T 7714 | Qiu, Yanqi,Wang, Zipeng. Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes[J]. JOURNAL OF FUNCTIONAL ANALYSIS,2022,282(1):45. |
| APA | Qiu, Yanqi,&Wang, Zipeng.(2022).Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes.JOURNAL OF FUNCTIONAL ANALYSIS,282(1),45. |
| MLA | Qiu, Yanqi,et al."Hyper-positive definite functions I: Scalar case, branching-type stationary stochastic processes".JOURNAL OF FUNCTIONAL ANALYSIS 282.1(2022):45. |
入库方式： OAI收割
来源：数学与系统科学研究院
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